few_shots: Example:
Problem/activity:
Task
Cruz and Erica were both getting ready for soccer.
Cruz ran 1 lap around the school.
Erica ran 3 laps around the playground.
Erica said,
I ran more laps, so I ran farther.
Cruz said,
4 laps around the school is 1 mile, but it takes 12 laps around the playground to go 1 mile. My laps are much longer, so I ran farther.
Who is right? Draw a picture to help you explain your answer.


Standard options: 
A. Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
B. Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model.
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.


Thought: This task asks students to compare two fractions that are equal. The two fractions have different numerators and denominators (e.g. 1/4 and 3/12). The students need to explain why the two fractions are equal by drawing a picture, which involves using visual fraction models.
Answer: A, B

Now, assign the following problem or activity to one or more relevant standards it aligns with.
shot_info: im_task_000212

4
options: Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.  For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.

For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.

Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
problem_activity: Activity
If students also use technology to create the tables, they are using appropriate tools strategically (MP5).
Launch
Provide access to graphing technology. Students may need some assistance adjusting their graphing window to see the relevant features of each graph. Either help them set the window before they start to a domain of
\(\text-2 \le x \le 8\)
and range of
\(\text-60 \le y \le 600\)
, or wait until they have attempted to graph at least one function and remind them of what they have learned about changing the graphing window.
Student Facing
Each function represents the amount in a bank account after
\(t\)
weeks.
\(A(t) = 500\)
\(B(t) = 500 + 40t\)
\(C(t) = 500 - 40t\)
\(D(t) = 500 \boldcdot (1.5)^t\)
\(E(t) = 500 \boldcdot (0.75)^t\)
Make a table for each bank account showing the money in the account at 0, 1, 2, and 3 weeks.
Describe in words how the money in the account is changing week by week.
Use technology to create a graph of each function. How can you see your description in each graph?
Student Response
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Activity Synthesis
Focus the discussion on the connection between the equations, descriptions and graphs. Discuss questions such as:
“What do all functions have in common?” (The vertical intercept is 500, each bank account starts with $500)
“How does the money change each week? How do we see this change in the graph?"
“How are
\(B\)
and
\(C\)
the same and different?” (They are the same because they are each linear, and each start with
$
500 and change by
$
40 per week. They are different because B increases and C decreases (or the rate of change is positive versus negative.)
“How are
\(D\)
and
\(E\)
the same and different?” (They are the same because they are each exponential, and each start with
$
500. They are different because
\(D\)
increases and
\(E\)
decreases (or the growth factor is greater than 1 versus less than 1.))


correct_option_index: 1